The following references are considered to be pertinent for the purpose of understanding the background of the present invention:    [1] G. Muller, M. Muller, A. Wicht, R. H. Rinkleff, and K. Danzmann, “Optical resonator with steep internal dispersion,” Phys. Rev. A 56, 2385-2389 (1997).    [2] M. Soljacic, E. Lidorikis, L. Vestergaard Hau, J. D. Joannopoulus, “Enhancement of microcavities lifetime using highly dispersive materials,” Phys. Review E. 71, 026602 (2005).    [3] Damian Goldring, Uriel Levy and David Mendlovic, “Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide—Design and analysis”—Optics Express, 15, 3156-3168 (2007)    [4] R. A. Soref, B. R. Bennet, “electro-optical effects in silicon”, IEEE J. of Q. Elec. QE-23, 123-129 (1987)    [5] A Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high speed silicon optical modulator based on metal-oxide semiconductor capacitor”, Nature 427, 615-618    [6] S. Stepanov, S. Ruschin, “Modulation of light by light in silicon-on-insulator waveguides” App. Phy. Lett. 83, 5151-5153 (2003).
An electro-optical (EO) modulator is an essential component in any optical communication system. An EO modulator is an optical device in which a signal-controlled element is used to modulate light using the electro-optic effect. The phase, the frequency, the amplitude, or the direction of the input light may be affected (modulated). The main features usually required for the EO modulator are high speed, sufficient modulation depth, low losses and, as with any other device, robustness and reliability. The EO modulator may be used for intra-chip communication, in which high speed, small volume, and CMOS process compatibility are required.
Traditional modulators are based on free space optics technology using, for example, polarization rotation. As technology advanced, different types of integrated EO modulators were demonstrated. Most of the modulators are based on either a Mach-Zehnder Interferometer (MZI) configuration, or on a resonant configuration (Fabry-Perot, Ring, etc). In both cases, an electrical signal is used to modulate the free carriers' concentration in the semiconductor to obtain optical modulation. Usually, a semiconductor EO modulator changes the resonant property of a resonator corresponding to an operating wavelength by controlling free carriers of a semiconductor, so as to serve as an optical switch and accordingly to enable rapid transmission of digital signals.
Optical resonators are devices having internal optical path lengths that are much longer than their physical dimensions. Long optical path lengths are produced by multiple reflections of optical rays on minor surfaces.
Two fundamental types of optical resonators are the Fabry-Perot cavity and the ring resonator. The Fabry-Perot cavity comprises two spaced-apart parallel reflective planes. Resonance (constructive interference of the reflected light) occurs for specific wavelengths of light reflected between the reflective planes, when a wave traveling in the resonator undergoes a 2πN phase retardation, where N is a whole number. Thus, the transmission resonances are periodic across the spectrum (assuming non-dispersive medium). Instead of reflective planes, reflective gratings can also be used to achieve similar results.
Ring resonators establish resonances in a similar manner, but the distance between the reflective planes is defined by the circumference of a circular waveguide rather than the separation between two reflective planes. The potential applications for such resonators include filters, sensors, optical delay lines, and more.
An important characteristic of optical resonators is its Quality factor (Q-factor) that is inversely proportional to the photon lifetime in the resonator (in time domain). Different applications require different Q-factor values; however, obtaining higher Q-factors for a resonator is typically of high interest. The overall Q factor of a resonator is given by 1/Q=1/Qabs+1/Qrad+1/Qc where Qabs, Qrad, and Qc are the absorption, radiation and coupling quality factors, respectively. Each of the Q-factor terms can be effectively increased by using a highly dispersive material inside the resonator [1, 2].
As for the materials used for the fabrication of the EO modulators, high-index materials (n≈3.5), such as silicon, enable strong light confinement and the fabrication of dense optical circuits. The horizontal confinement of the light is generally obtained by different patterns that are introduced to the substrate, while the vertical confinement is usually created by a low-index or highly reflective layer. For example, for Silicon-On-Insulator (SOI)-based devices, having generally a silicon substrate (Si) layer, and a top cladding (SiO2) layer, the horizontal confinement is created by the difference between the index of refraction of the air and of the SiO2 (n≈1.5).
The optical properties of the silicon are expressed via its complex refractive index. In order to tune the optical characteristics of a SOI-based device, the silicon's refractive index has to be changed, by using, for example, the electrically induced method.
The method for electrically inducing refractive index changes in silicon is based on the modulation of the free carriers' concentration. Free carriers are generally electrically injected to a silicon substrate using a PN junction or a MOS capacitor. The injected carriers produce a change in the silicon's refractive index due to three major effects: (i) free-carrier absorption, (ii) Burstein-Moss effect, and (iii) Coulombic interaction with impurities.
An analytic approximation to refractive index change (according to the Drude Model) is given by [4]:
                              Δ          ⁢                                          ⁢                      n            FC                          =                              -                                                            ⅇ                  2                                ⁢                                  λ                  2                                                            8                ⁢                                                                  ⁢                                  π                  2                                ⁢                                  c                  2                                ⁢                                  ɛ                  0                                ⁢                n                                              ⁢                      (                                                            Δ                  ⁢                                                                          ⁢                                      N                    e                                                                    m                  ce                  *                                            +                                                Δ                  ⁢                                                                          ⁢                                      N                    h                                                                    m                  ch                  *                                                      )                                              (        1        )            where ΔNe, ΔNh are the changes in the free electrons and holes concentrations respectively, and m*ce, m*he are the effective masses of free electrons and holes respectively. The analytic approximation indicates the phenomenological behavior of the silicon, however, for more accurate calculations, the empirical equation (2) experimentally derived in reference [5] for 1.55 μm wavelength is used:ΔnFC=−8.8×10−22ΔNe−8.5×10−18(ΔNh)0.8  (2)The electrons and holes densities are in cm−3 units.
Performing analytical calculation of the concentration of free carriers that are injected to a SOI-based device is rather difficult. Basically, the continuity equation is solved for the charge carriers, and the generation rate in case of illumination is calculated [6]. The major obstacle in such a process is the surface recombination which has a strong influence on the charges distribution. Since surface conditions vary from one device to the other, and depend greatly on fabrication processes, it is very difficult to predict the charges distribution. In order to get some approximate results, one may use previously obtained results or perform some preliminary experiments.